Abstract

Integrated photonics via Si CMOS technology has been a strategic area since electronics and photonics convergence should be the next platform for information technology. The platform is recently referred to as “Si photonics” that attracts much interest of researchers in industries as well as academia in the world. The main goal of Si Photonics is currently to reduce material diversity of photonic devices to pursuing CMOS-compatibility. In contrast, the present paper proposes another route of Si Photonics, reducing diversity of photonic devices. The proposed device unifying functionality of photonics is a microresonator with a pin diode structure that enables the Purcell effect and Franz-Keldysh effect to emit and to modulate light from SiGe alloys.

1. Introduction

Electronic and photonic integrated circuits (EPICs) on Si complementary metal oxide semiconductor
(CMOS) platform have widely been studied to achieve higher figure-of-merits in
communications and computations. A challenging issue is that there are so many
kinds of devices in photonics as in Table 1. The photonic devices have been developed for optical
communication systems in which integration of these devices on a chip has never
been important. Thus, the concurrent photonics consist of various devices (materials)
such as light emitters (III-V semiconductors), modulators (LiNb), interconnects
(Si), filters (Si), photodetectors (III-V
semiconductors), and isolators (YIG). On the contrary, electronics as in Table 1 consists only transistor and interconnect; and the material systems are all
compatible to the CMOS fabrication process referred to as “CMOS-compatible.” Si
photonics today have focused on reduction of the material diversity by fabricating these
photonic devices with CMOS compatible materials. In the present paper we will
propose a new approach: functional
unification of photonic devices. The enabler of the unification is the
materials system of Si waveguide and Si. The features of the
system are as follows:(i)polarity and conductivity
control of Si waveguides by implementing pin diode structures,(ii)high-index contrast to Si acting as cladding and electrical insulation that reduces device
footprints. To utilize these features, the proposed novel device is based on a microresonator with a built-in pin
diode. Physics presenting emitter and modulator functions are the Purcell
effect [1] and Franz-Keldysh effect [2].

Table 1: Device and material
diversity of electronics and photonics.

2. How to Reduce Device Diversity

The Purcell effect is known to
enhance spontaneous emission rate on a resonance wavelength of a microresonator,
as schematically shown in Figure 1(a). There have been various papers reporting
the effect is actually working based on standing wave resonators [3, 4] and
traveling wave resonators [5, 6].
On the other hand, electro-optic effect such as the plasma effect or
Franz-Keldysh effect is known to change the complex refractive indices of the
resonator materials, which functions to modulate optical amplitudes by shifting
the resonance wavelength as also schematically in Figure 1(b). Here, we would
propose a new device to unify several photonic functions in Table 1. The device
is a resonator with a pin structure as in Figure 1(c). Forward-biasing of the
resonator would function as a light emitter due to the Purcell effect; and
reverse-biasing would function as a modulator due to the Franz-Keldysh effect.
The device is referred to as a unified functional device (UFD) in the present
paper. UFDs should in principle function as a light emitter, an amplifier, a modulator,
a switch, as well as a tunable filter. Accordingly the device diversity of
photonics in Table 1 is to dramatically shrink and the device set for photonic
integration is only UFDs, detectors, and interconnects. Isolator function is not
yet available.

3. Physics and the Requirements to Unify the Device Functions

In this section we will discuss
physics, materials, and structures of UFDs.

3.1. Purcell Effect and the Requirements to Ring Resonators

We first consider a single localized radiating dipole;
its spontaneous emission rate can
be expressed via the Fermi golden rule; where is the
Planck constant, is the density of
optical modes (states) at the emitter’s angular frequency. Considering the
dipole moment , and the electrical vector , the term can be simplified as . The matrix element depends on the band structure of the media, we just refer to it as for simplification later. When is parallel to ,
the spontaneous emission rate can be expressed in the following well-known
form:
Here, and
are the electron density of the conduction band and valence band expressed by
Fermi-Dirac statistics. denotes the mode density in a unit of angular
frequency. Equation (2) indicates that depends on the initial electron—and hole density of states and the final
photonic density of states. The quantum confinement focuses on increasing while the microresonator on controling .

When the modal volume of the resonator is very large, the optical mode is continuous in
the -space. Assuming the distribution of the electron is uniform all around
the structure, can be expressed as where denotes
the center of the spontaneous emission band, the average dipole momentum, the effective refractive index of the
resonator. Considering a small resonator with the scale of the emission wavelength , the modes will be quantized in the -space. Meanwhile, the electrical field will increase with resonator size reduction. The emission rate at the resonance
wavelength can be derived as where is the
relative confinement factor, expressing the overlapping between the optical
mode and the resonator structure, and can be 1 in the high-index contrast
systems. Here, is the modal volume, and is the larger one of or the full
width at half maximum (FWHM) of resonance mode (). Since spontaneous emissions are generally
broader than the resonance modes, then ; . Here, we assumed the resonance frequency is at the center of the spontaneous
emission band.

Finally,
the enhancement of the spontaneous emission rate usually called Purcell factor can be expressed by
comparing the emission rates in the small resonator and space: In silicon resonators, the other
factors expect and are all state constant. The higher , the higher Purcell
factor. According to Zsai et al., we need to get an enhancement factor of
nearly 100 to get positive net gain when the loss is due to free-carrier
absorption [7]. So, our requirement of the Purcell enhancement is at
least 100.

3.2. Franz-Keldysh Effect and Requirements to Unify Device Functions

Si and Ge have the inversion symmetry in the lattice, prohibiting the existence of a
linear electro-optic effect. Thus, the bias applications to the pin diode
structures have been employed to change in carrier concentration and/or
electric field strength and eventually altering refractive indices of the
structures. The Franz-Keldysh (FK) effect is a typical one having been used in
III-V semiconductor-based modulators. However, the effect was ignored until
recently in Si, since the effect in Si was known very weak. We have recently
reported that Ge shows a large electro-optic coefficient induced by the FK
effect. The difference from Si can be explained by the difference in the band
structure of Ge where the point causing the FK effect is only slightly
above the valley.

The FK effect occurs as follows: the change in dielectric constant () at energy under the field is
given in terms of the well-known FK expressions and containing Airy functions and their
derivatives [8, 9]: Here, represents transition probability by absorption of photon,
containing matrix element
and reduced effective mass . is Planck’s constant divided by . In our model, we considered the FK effect
from the direct band edge as noted above. The contribution from the indirect
band edge was ignored in this treatment.

According to a simple mathematics,
the following relations can be derived: Here, denotes the
shift of resonance wavelength , and denotes the shift of refractive index . Assuming that of the resonator in Figure 1 is 4000, and that should be
when is 4.0, that is, Ge, the modulation depth can be 50 dB or
higher, which is more than enough. However, we will find out that is the realistic limit in terms of FK effect as shown later. So, we set our
goal of index change to be mid . Thus, of must
be required.

3.3. Ring as a Microresonator

There are two kinds of microresonators utilizing traveling waves and
standing waves. We have employed traveling wave resonator to demonstrate the
feasibility of UFDs since it is expandable to a three-terminal device. In the
traveling wave resonator, we have further chosen ring resonators instead of
disks because of fewer mode numbers involved in the resonator. In general, the
observed can be written by [10] Here, is the observed ,
loss of the ring itself, and coupling between the waveguide and ring. In case of isolated ring resonators, . Thus, can be
expressed as Here, denotes the
overall attenuation coefficient of the ring, usually consisting of material
absorption and attenuation due to light scattering of the ring waveguide.

These are simple explanations to
control device functions and requirements for UFDs to function.

4. Results

In this
section, we will present the simulation and experimental demonstration of the characteristics of ring resonators
functioning as
light emitters and modulators. We have not yet prototyped those with pin diode
structure. The resonators were fabricated on Si on insulator (SOI) wafers by
means of electron beam (EB) lithography and dry etching (DE) [6, 8, 11].
The SOI wafer has a 3 m buried oxide (BOX) layer and a 200 nm
top Si layer. The waveguides used to verify the feasibility of UFDs have 400 nm
width and 200 nm height where the transverse mode is single. The radius ranged
from 2.6 to 10 m. The gap between
incoming waveguide and the ring was changed from 150 nm to 350 nm. The gap
between outgoing waveguide and the ring is identical to the one between the incoming
waveguide and the ring. The SEM image of the fabricated sample is shown as
insert in Figure 2. The waveguides for emission function have 250 nm width and
370 nm height. The excitation is done by ion laser irradiation
focusing on the waveguide. The resonator is isolated, and light escaping from
the ring is collected using optical microscope.

Figure 2: Transmission spectra of the ring resonator and and versus ring radii. is quality factor and is the number
of wavelengths in the longitudinal ring mode.

Figure 2 shows and of the various sizes of rings to check if
the requirements described in Section 2 would be met. has to be larger than
for FK requirement for modulator. The cavity volume is , thus the
term of in (5) can be simplified by , where denotes the number of the wavelength
in the longitudinal mode of interest. To meet the requirement of 10–100 time Purcell
enhancement, .
Figure 2(a) shows transmission spectra of the through port and drop port of the
ring resonator, m and gap =
300 nm. From the transmission spectrum of the drop port, is determined to be
nearly 50 000. It is also clear from Figure 2(b) that the rings fabricated have
met the Purcell requirement as well as the FK modulation when the radius is 2.6–10 m.

4.2. Purcell Enhancement of Spontaneous Emission of the Ring Resonator

Figure 3
shows the photoluminescence spectra of (a) the isolated Si ring resonator with
the radius of 3.2 m and the width of 250 nm and of (b)
the slab region surrounding the ring. The luminescence of the slab in Figure 3 is
multiplied by 10 to show it in this linear scale range. The luminescence
consists of many peaks and the highest peak is more than 100-times stronger in
intensity than the luminescence of the slab. The wavelengths of all peaks show
a clear one-to-one correspondence with the resonance frequencies of the ring.
Figure 4 shows the luminescence enhancement observed and the Purcell factors
calculated by (5). The experimental data are in a good agreement with the
prediction, indicating that the enhancement would occur due to the Purcell
Effect. The enhancement is 10 times which is lower than our requirement of ring resonator. We
will discuss this point later on.

Figure 3: Photoluminescence spectra
of (a) ring and (b) surrounding slab. The ring is 3.2 m in radius. The peaks are
generated at the resonance wavelengths.

4.3. Resonance Shift Using FK Effect

The Ge p-i-n photodiodes used in this work were fabricated from 1.3 m thick undoped Ge epilayers on a Si(100) substrate with boron concentration cm−3.
The Ge epilayer was under 0.20% tensile strain [12]. Phosphorus was
implanted into a poly-Si layer that was deposited on the top of the Ge epilayer
to create a pin diode. External biases of 0 and 5 V were applied to the diode,
corresponding to electric fields of 14 and 70 kV/cm in the Ge i-layer. The
absorption coefficient α was
calculated from the photodiode responsivity () defined by photocurrent normalized by incoming light power in
A/W. Figure 5 shows the absorption coefficients extracted from the spectral
responsivity. As predicted by the FK effect, the absorption coefficient
increases with the applied electric field.

Figure 5: Absorption coefficient spectra under electric-field applications. The experiments are well reproduced
by the Franz-Keldysh analysis.

We have incorporated the strain effect into our Franz-Keldysh model to analyze the data
as in Figure 5. The excellent fitting of the experimental data to the model
obtained, suggesting that the change in absorption coefficients is due to the
Franz-Keldyshi effect in the strained Ge epilayer on Si. Based on the
Kramers-Kronig relation, we have derived the dependences of refractive indices
difference and absorption coefficient α as a function of wavelength as in Figure 6.
Figure 6(a) shows as a parameter of electric field
strength, 20, 50, and 100 kV/cm. It is found that the electric field strength
20 kV/cm is not enough to change refractive index, mid to enable
modulator function. The Ge pin diode for under electric field strength 50 kV/cm
can realize such index change in the wavelength range of 1750 nm or shorter.
However, the absorption coefficient gets larger in the wavelength range as in
Figure 6(b) and it is less likely that should exceed according
to (9). Indeed, Figure 6(c) indicates that
should be mid at 1700 nm that is lower than the requirement
discussed above. As in Figure 6(c), of the Ge ring under 100 kV/cm can reach at 1850 nm. This lead us to conclude that the Ge-based ring can be operated as a
modulator at 1850 nm under the electric field, 100 kV/cm.

5. Discussion

We have shown the microring resonators can unite the photonic functions ranging
from emitter, modulator, as well as filter. This suggests it can function as
amplifier, and switch. This substantially reduces device diversity in
Photonics. Since materials used in the UFDs are Si or Ge, that is,
CMOS-compatible, the presented approach reducing device diversity should be
beneficial for large-scale integration of electronics and photonics on a Si
chip. However, the presented UFDs require two material systems Si and Ge for
resonators although these are on the same
materials platform. In this section, we will consider the feasibility of
materials unification via SiGe as the resonator materials to unify the emitter
and modulator functions.

5.1. SiGe UFDs

Because of low absorption coefficient resulting in high , both of the Purcell
enhancement and the FK shift are
large at the photon energy slightly below gap, like 1200 nm for Si. According to
the literature, Ge-rich SiGe, for example, the Ge composition 0.95
should be of such materials. The indirect bandgap is
around 0.8 eV, the communication wavelength band called C- and L-band, and the direct bandgap
referencing the FK effect is 1.0 eV [9]. The tensile strain of Ge on
Si reduces the direct gap to 0.9 eV, as in Figure 7. The reduction of direct
bandgap observed was in a good agreement with the deformation potential
calculations [13]. Because of tensile-trained SiGe, we would be able
to design UFDs built on the unique material system. This will be reported in a
separate paper.

Figure 7: The direct bandgap versus SiGe alloy composition. The reported data were taken from bulk Ge using electroreflectance. Our data based on
photoreflectance shows smaller direct bandgap in terms of tensile-strain in Ge
epi on Si.

5.2. Increase of Luminescence Enhancement

The Si ring
resonator emits strong light at the resonance wavelengths at the indirect band
edge, 1.1 m. The
enhancement we obtained was about 10 as in Figure 4. To get higher enhancement,
we need to increase . Although of the isolated ring is not ready for
measurement, the Purcell analysis leads us to estimate that is as low as
500, corresponding the overall attenuation coefficient to be 180 cm−1 according to (9), assuming the group velocity is cm/s and
wavelength 1.1 m. It is
clear that the attenuation cannot be material absorption, 1.3 cm−1 at
1.1 m. It has
been pointed that the sidewall roughness should increase the attenuation
coefficient and could explain 180 cm−1. According to Soref and Bennett [14],
free-electron absorption is 1 cm−1 at the density of /cm3 at 1.1 m and free
holes do almost the same. When the ring resonator is excited to measure
photoluminescence, a high density of carriers if it is in concentration of cm−3 would result in such loss in terms of in free-carrier
absorption. should be
reduced unless otherwise. Therefore, passivation of Si waveguides such as
hydrogenation, and oxidation should be indispensable for UFDs.

6. Conclusion

A new
approach on electronics and photonics convergence on Si CMOS platform is
proposed; reducing device diversity rather than material diversity in
photonics. The device concept unifying functional devices is a microresonator
with a pin diode structure, and is theoretically and experimentally studied. It
has been shown that the Purcell effect and the Franz-Keldysh effect should
enable devicing the concept to unite photonic functions such as emitter,
amplifier, modulator, switch, and filter. It is further discussed that Ge-rich
SiGe would be the material system for UFDs. The present approach simplifies
photonic devices to UFDs, photodetectors, and interconnects, that will be
beneficial for large-scale integrated electronics and photonics circuits.

Acknowledgments

The authors acknowledge Dr. Christina Manolatou in Cornel University for the FDTD simulator code. The work
was partly supported by Grant-in-Aid for Creative Scientific Research by
Japan Society for the Promotion of Science. The
devices were fabricated at the NTT Microsystem Integration Laboratories, by the
University of Tokyo VLSI Design and Education Center's (VDEC) 8-inch EB writer
F5112+VD01 donated by ADVANTEST Corporation with the collaboration of Cadence
Corporation, and at Massachusetts Institute of Technology. The authors are grateful
to Drs. K. Yamada, T. Tsuchizawa, T. Watanabe, and S. Itabashi at NTT Microsystem Integration
Laboratories, and to Drs. J. F. Liu, S. Jongthammanurak, J. Michel, and L. C. Kimerling at Massachusetts Institute of Technology
for their in-depth discussions. The authors also like to thank Dr. Y. Ishikawa, Mr. S. Y. Lin, and Mr. P. H. Lim.